Step One: Find the vertex point (h,k) (the lowest or highest point in the graph on the axis of symmetry) and any other point (x,y) along the parabola
Step Two: Using the vertex point and another point in the parabola, use the equation y=a(x-h)^2+k substitute the vertex point for h and k and the other point for x and y
Step Three: Solve for a in the equation
Step Four: Rewrite the equation using the vertex point and a in the equation to get your final equation.
Example:
y=a(x-h)^2+k
vertex(2,1)
Other point(1,0)
Step Two: Using the vertex point and another point in the parabola, use the equation y=a(x-h)^2+k substitute the vertex point for h and k and the other point for x and y
Step Three: Solve for a in the equation
Step Four: Rewrite the equation using the vertex point and a in the equation to get your final equation.
Example:
y=a(x-h)^2+k
vertex(2,1)
Other point(1,0)
(0)=a((1)-(2))^2+(1)
0=a+1
a=-1
y=-1(x-2)^2+1
This example does not match the equation, but is an example of a parabola.
Graph compliments of http://www.regentsprep.org/Regents/Math/conics/LPara.htm
This topic is connected to the others because they all involve parabolas, graphing, vertex points, axises of symmetry, and equations of parabolas.